Birds of a
Feather Flock
Together:
A Study of DoctorPatient Matching
Geir Godager
Institute of Health Management
and Health Economics,
Health Economics Research
Programme, University of Oslo
UNIVERSITY
OF OSLO
HEALTH ECONOMICS
RESEARCH PROGRAMME
Working paper 2009: 3
HERO
Birds of a Feather Flock Together:
A Study of Doctor-Patient Matching
Geir Godager
27. April 2009
Health Economics Research Programme at the University of Oslo
HERO 2009
Keywords: GP services. Discrete choice. Willingness-to-pay. Health care demand.
JEL classification: C25, C83, D12, I11
Author:
Geir Godager, Institute of Health Management and Health Economics, Health Economics Research
Programme, University of Oslo, P.O. Box 1089 Blindern, 0317 Oslo, Norway. Telephone: (+47) 22 84
50 29, fax: (+47) 22 84 50 91. E-mail: geir.godager@medisin.uio.no
Health Economics Research Programme at the University of Oslo
Financial support from The Research Council of Norway is acknowledged.
ISSN 1501-9071 (print version.), ISSN 1890-1735 (online), ISBN 978-82-7756-203-2
Abstract
In this paper we study individuals' choice of general practitioners (GPs) utilizing
revealed preferences data from the introduction of a regular general practitioner scheme in
Norway. Having information on relevant travel distances, we compute decision makers' travel
costs associated with different modes of travel. Choice probabilities are estimated by means
of nested logit regression on a representative sample of Oslo inhabitants. The results support
the general hypothesis that patients prefer doctors who resemble themselves on observable
characteristics: Individuals prefer GPs having the same gender and similar age.
Specialist status of GPs was found to have a smaller effect on choice probabilities than other
attributes such as matching gender. When travel costs are calculated by means of taxi prices,
the estimated willingness to pay for specialist status of a GP amounts to € 0.89 per
consultation, whereas the estimated willingness to pay for having a GP with the same gender
amounts to respectively € 1.71 and € 3.55 for female and male decision makers, respectively.
1. Introduction and background
When a patient consults a physician in an event of illness, the first of the physician’s tasks is to reveal is the cause of illness, i.e. the diagnosis. A second task
is to recommend an appropriate treatment and ensure that the patient is compliant with the treatment. Communication between the physician and the patient is
an important element in both these processes. If the information transmission is
efficient such that physician and patient are able to communicate easily and understand each other, the physician may be more likely to succeed in setting the
correct diagnosis than if the converse was true. One may also argue that mutual
confidence and unconstrained communication may cause the treatment to be more
effective, as the degree of patient compliance is likely to be higher if the patient
receives and understands the information relevant for the treatment. Often the
doctor-patient relationship is described as a one of imperfect agency with the patient as the principal and the doctor as the agent. As described by Scott (2000,
p.1179) the communicative ability of the matched doctor-patient unit is likely to
affect the cost structure and the efficiency of a consultation, and transmission of
information is thus likely to play a central role in meeting the objectives of the
patient. The process of choosing a health care provider may thus be understood
within the context of an agency paradigm, where part of the consumer’s objectives
is to affect the degree of imperfect agency, as suggested by Scott and Vick (1999).
The consumer (principal) may mitigate agency imperfections by choosing a matching doctor (agent). We follow this idea and assume that patients prefer GPs who
resemble themselves with respect to observable characteristics. This application of
the old saying that “birds of a feather flock together” is shown to be a useful guide
in the empirical specification where we model a representative decision maker’s
choice of GP within the random utility framework. The basic idea of this modeling
framework is that a decision to choose a particular GP is considered the outcome of
optimizing behavior, and a particular GP is chosen because the associated utility
is higher than that of other alternatives.
The determinants of practice choice are examined in several studies, as reviewed
in Scott (2000). Most earlier studies involving choice analysis and matching of
GPs and patients consist of analysis of individuals’ stated preferences with regard
2
to hypothetical GPs. Examples of studies based on choice experiments are Scott
and Vick (1998), Scott and Vick (1999), and Ryan et al. (1998). In these studies
discrete choice experiments is applied to estimate the relative impact of different
attributes of hypothetical GPs. While there are some obvious advantages with
generating data in a controlled environment with appropriate sampling design,
there are also drawbacks: The results are shown to be sensitive to the design and,
in particular, the level of the attributes are shown to affect estimates of willingness
to pay (Ryan and Wordsworth, 2000). Even though discrete choice experiments
leave some important value judgments to the researcher, few studies use data on
patients’ revealed, rather than stated preferences. One example is Dixon et al.
(1997), who examine the determinants of the rate at which patients left practices
in three English health authorities. This study focuses on patients who revealed
their preferences by switching practice without changing their home address. The
main findings are that patients are more likely to leave a practice if it is small, if it
is associated with longer travel distance and if it has shorter opening hours. They
also find that 38 percent of the patients are registered with the practice closest to
their home. Applying Norwegian data Lurås (2003) studies the consumers’ ranking
of GPs and find that individuals prefer GPs who are specialists as compared to GPs
without specialist status. Other results are that consumers prefer a GP with the
same gender, and that choice probabilities are found to be declining in the age
difference between GP and patient.
An important feature of the latter studies is that endogenous sample selection is
not accounted for even though one may argue that it is not obvious that individuals
showing active switching behavior are representative for the general population.
The present paper contributes to the literature by utilizing revealed preferences
data in a setting where we are able to account for the potential selection bias
resulting from endogenous sample selection. Having access to data describing the
total population we are able to construct a representative sample of decision makers
by means of the propensity score matching method. This material is well suited
to study how attributes of GPs such as age, gender and specialization affect the
individuals’ choice of GP. The results from estimation of a nested logit model
support the hypothesis that patients prefer GPs who resemble themselves with
respect to observable characteristics. Individuals are more likely to choose a GP
3
with the same gender, and the estimated choice probabilities are declining in the
age difference.
The paper proceeds as follows. In Section 2 we give a brief description of the
Norwegian reform of general practice. Data and sampling strategy is described
in Section 3 while the econometric model is specified in Section 4. Results from
estimation are given in Section 5 while Section 6 concludes and discusses the policy
implications of the findings.
2. Institutional setting
The data used in this study is from Norway, a country with a national health
service financed mainly through general taxation. A nationwide introduction of a
regular general practitioner scheme in 2001 serves as a natural experiment providing detailed data on individuals’ preferences for GPs. In order to implement this
list patient system, every inhabitant was asked to return a response form ranking
their three most preferred GPs in descending order. Since the submitted ranking
information was intended to be used in the actual matching process forming each
GP’s patient list, this material constitutes a unique source of information on individuals’ revealed preferences for GPs. Under the new scheme, more than 90% of the
GPs are self-employed, with a payment system consisting of 30% per capita payment from the municipalities and 70% fee for service payment. The latter includes
out of pocket payment from patients paying a fixed fee per consultation (e 14.70
in 2001), with an annual ceiling. A special feature of Norwegian general practice
is that two types of general practitioners exists: some have status as specialist in
general medicine, the remaining do not have this status. GPs with specialist status
are entitled to a higher consultation fee. The additional fee (e 6.80) is financed by
the National Insurance Administration. In order to achieve the formal specialist
status the physicians are required to have more than four years of work experience
in general practice, one year of experience from an inpatient or outpatient hospital
department, and further, they need to fulfil a post-graduate education programme.
This programme consists of courses, seminars and supervision from a senior GP.
If one believes that more education adds to GP quality, specialist status may be
considered to be an observable indicator of quality. Admittedly however, knowledge on specialist status of GPs is information that most likely is not acquired
4
by every decision maker. In the same way that we expect costs to affect choices
in situations were costs are hard to calculate1 , it is meaningful to investigate the
impact of this attribute on choice probabilities. The reason is that the aim is to
model the behavior of a representative decision maker. In summary, the market
under consideration may thus be described as one where traded goods have observable quality differentiation and no consumer price variation, as the patients’ out of
pocket payments were the same for both types of GPs. An interesting question is
then, does specialist status affect the demand for GP services, and if so, what is
the magnitude of this effect?
3. Data and sampling strategy
Our data set is provided by the Norwegian Social Science Data Services. The
observation unit is the individual inhabitant. All inhabitants in 14 Norwegian
municipalities are included in the original data set. In this paper we will only use
observations from inhabitants and GPs in the city of Oslo. The main reason for
this decision is that an extract, containing the data from this densely populated
metropolitan area gives more precise information on travel distances, compared to
data from more rural areas where large geographical areas share the same postal
code. As we know the residential addresses of consumers and practice addresses
of GPs, a measure of the relevant travel distances in kilometers and travel time in
hours can be added from a drive-time matrix.2 One may argue that a limitation of
this study is that we do not have exact information on the travel distances of each
consumer. However, other methods of gathering information on travel distances
would most likely also be imperfect. Further, the fact that Oslo has more than 400
unique postal codes, and that the distance matrix has recorded travel distances as
short as hundred meters suggest that the measurement errors are small.
We are interested in studying the choice of sovereign consumers. Since parents
are likely to choose the GP for their children we exclude observations of consumers
1
2
Examples include phone rates, electricity tariffs and costs associated with car travel, etc.
The private company Infomap Norway has collected actual travel distances and travel times
associated with travel by means of a “light truck” on public roads between centers of the postal
code areas.
5
younger than 18. After the exclusion of some observations where relevant information was missing, our sample has 401999 unique observations, of which 68%
participated in the choice process. Descriptive statistics of the decision makers are
given in Table 1. In the left column we give a description of the adult population
of Oslo residents. The variable unemployed is a dummy variable equal to 1 if
an individual received any unemployment benefits in the period 2000-2002, and
we se that see that 10% of the adult population has received such benefits. The
variables net wealth and income consist of 10 groups categorized according to
the deciles in the 14 municipalities. From the statistics on variable net wealth
we see that 10.5% of the population has a net wealth lower than the first decile,
and we see that 10.3% has a net wealth between the first and second decile.
Only observations of individuals who returned the response forms, henceforth
referred to as participants, can be used when estimating our choice model in Section
5. Individuals who did not take part in the GP choice process, henceforth referred
to as non-participants, will therefore be excluded. As can be seen by comparing
the three columns in Table 1, the consumers who participated in the choice process
do not seem to be a representative sample of the inhabitants in Oslo.3 We observe
that a larger share of females returned their GP preferences as compared to males.
We also observe that individuals with many years of schooling and high income are
over-represented among participants, while younger individuals and people born
in a foreign country, and people who have received unemployment benefits in the
years 2000-2002 is clearly under-represented. The situation at hand has similarities
with the sample selection situation described by van de Ven and van Pragg (1981).
They study the demand for deductibles in private health insurance applying survey
data where a large share of individuals returned incomplete questionnaires. They
develop a two part binary probit model with endogenous sample selection in order
to address the issue that the unobserved, and hence omitted, variable “expected
medical expenses” is likely to relate both to the probability of completing the questionnaire, and to the probability of preferring a health insurance with a deductible.
In the current situation one might suspect that the decision maker’s state of health
is related both to the probability of submitting provider preferences, and to the
3
Confront Table A.1 in the appendix for a description of geographic representation in Oslo
6
Table 1: Descriptive statistics for exogenous variables
Population versus a self-selected and a corrected sample
sample
Variable
population
N=401999
Proportion
self-selected
n=15000
Proportion
corrected
n=15000
Proportion
Female
Unemployed
Non-nordic
0.522
0.101
0.154
0.581
0.082
0.123
0.520
0.104
0.156
Schooling
1-7 Years
8-10
”
11-12 ”
13
”
14
”
15-17 ”
18-19 ”
20+
”
0.006
0.138
0.220
0.206
0.023
0.251
0.098
0.008
0.005
0.148
0.237
0.199
0.023
0.252
0.099
0.009
0.006
0.145
0.228
0.207
0.022
0.241
0.096
0.008
age
30-40
40-50
50-60
60-70
70+
0.238
0.171
0.147
0.084
0.137
0.207
0.177
0.174
0.106
0.166
0.238
0.170
0.149
0.084
0.137
net wealth
deciles†
1
2
3
4
5
6
7
8
9
0.105
0.103
0.101
0.100
0.101
0.098
0.097
0.096
0.097
0.089
0.096
0.088
0.088
0.083
0.096
0.109
0.118
0.116
0.103
0.103
0.098
0.104
0.101
0.102
0.099
0.101
0.094
income
deciles†
1
2
3
4
5
6
7
8
9
0.100
0.094
0.097
0.097
0.098
0.099
0.101
0.102
0.104
0.081
0.090
0.095
0.105
0.104
0.104
0.109
0.106
0.106
0.096
0.098
0.094
0.102
0.098
0.100
0.101
0.103
0.103
† Deciles are calculated from the individual observations from 14 representative municipalities included in the original file.
Decile1 refer to proportion of individuals with wealth/income less than Decile1. Decile2 refer to proportion of individuals with
wealth/income between decile 1 and 2, etc.
relative valuation of the various attributes of GPs, such as GPs’ specialist status.
The empirical model is set up to model the decisions made by a “representative
7
decision maker”. If estimation is performed on a random sample from within the
subset of self selected participants, the result may be biased coefficients or coefficients with an unclear interpretation. If the estimate of coefficients and the average
willingness-to-pay is to have a meaningful interpretation, it is important that the
decision makers included in the estimation sample really are representative for the
population. As we are considering the choice between a large number of alternatives, the binary choice selection model considered by van de Ven and van Pragg do
not seem applicable to the situation at hand. However, as we have a large number
of observations and detailed information on the characteristics of both participants
and non-participants we have the opportunity to generate a representative sample.
Following Rosenbaum and Rubin (1983), we generate a representative sample of
Oslo inhabitants by applying the method of propensity score matching, replacing
non-participants with participants having approximately the same predicted participation probability.4 The procedure may be described as follows: Let S denote
the set of Oslo inhabitants, consisting of both participants and non-participants,
expressed by S = Sp ∪ Snp .
1. Estimate the probability of participation applying the total population, S, and
calculate the predicted participation probability ρ̂is , i = 1 . . . 401999, s = p, np
2. Draw a random sample s ⊂ S of n individuals and obtain a sample of both
participants sp and non-participants snp .
3. Replace the sampled non-participants, snp , pairwise with participants who:
(i) Are included in Sp but not included in sp , and
(ii) have approximately the same propensity score as the non-participants they
are replacing: ρ̂inp ≈ ρ̂jp
The results from the estimation of the participation probabilities are given in
Table A.2 , and the details from the matching routine is described in Table A.3
in the appendix. By comparing the means in the third column of Table 1 with
4
Representative samples can be achieved by beans of stratified sampling. Even though this is a
simple approach with a small number of strata, it is not feasible in our situation where the aim is
to account for a larger number of characteristics. The reason is that the number of distinct strata
becomes unmanageable as the number of variables, or categories within each variable, increase:
With 2 categories and V variables there are 2V distinct strata.
8
the corresponding means of the population we see that a more balanced sample is
achieved.
Table 2: Descriptive statistics for GPs. N=437
Variable
Mean
Std.dev
specialist
GP born in Norway
femaleGP
ageGP
marriedGP
0.53
0.80
0.38
47
0.66
0.50
0.40
0.49
7
0.47
The decision makers’ choice menu consists of 437 alternative GPs meaning that
437 GPs have been ranked as the most preferred GP by at least one inhabitant.5
In Table 2 we describe variables at the level of the GP. We observe that 53% of the
GPs in Oslo are specialists in general medicine, and that 80% of the GPs in Oslo
are born in Norway. Further, the average age of GPs in Oslo is 47 years and 38%
of the GPs are females, and 66% of the GPs are married.
Since travel is costly, we expect that GPs with practices that are located close
to the consumer’s residential address are preferred to GPs located further away.
We expect, ceteris paribus, the choice probabilities to be decreasing in travel time
and travel distance. In order to achieve a monetary measure of the travel costs, a
set of prices for distance and time is needed. A high-cost and a low-cost mode of
travel is suggested, corresponding to travel by means of taxi and travel by means
of private car. The fare schedule of the biggest taxi company in Oslo is used to
get costs associated with taxi travel. To compute the costs associated with travel
by means of private car a cost estimate of e 0.40 per kilometer is applied, which
also corresponds to the reimbursement rate used by the Norwegian public sector
to compensate employees for using their own car on official business.
The decision makers’ own time is also part of travel cost. The “shadow price
of time” is of course an individual specific variable and likely to be dependent of
age, health and employment status. This information is not available at the level
of the individual. A measure of the value of time spent on travel, as estimated
5
We thus ignore the small number of GPs not ranked as number one by any of the decision
makers.
9
by the Norwegian Institute of Transport Economics (Killi, 1999), is applied as the
monetary cost of the decision makers’ time use, although using such an aggregate
is of course not beyond critique. The formulas for calculating travel costs are
presented in Table 3. The travel costs associated with traveling to the GP is
multiplied with a factor of 2, since patients travel both back and forth.6
Table 3: Formulas for calculating travel costs
Applying the fare schedule (TAXI), and a reimbursement schedule for the public sector (CAR).
Mode
TAXI
CAR
Prices
start fee†
(0) 4.10
0
(e)/km
1.30
0.40
formula
(e)/hour‡
6.80
6.80
travelcosts = 2×[4.10+1.30*km+ 6.80*hrs]
travelcosts = 2×[ 0.40*km + 6.80*hrs ]
† Start fees are set to zero when distance is zero ‡ Inflation adjusted values for “time spent on travel” are from Killi (1999).
For given prices, the travel costs is a linear function of distance and time.
Traveling to the GP by taxi is of course more expensive than traveling by own
car, as the kilometer price is more three times as high. An equally important issue,
however, is the fact that these two modes of transport have different cost structures
as there is a starting fee required for each taxi trip.
In order to follow the idea that consumers prefer GPs who resemble themselves
on observable characteristics, our representative utility function specified in the
next section will include variables interacting characteristics of the alternative GPs
with corresponding characteristics of decision makers. In Table 4 we describe the
suggested interaction variables using the corrected sample of decision makers7 . We
compute the absolute value of the age difference between the patient and the GP,
agedifference. We see that the average age difference between consumer and the
selected GP is 16 years. Since an increase in agedifference implies that that the
patient and GP are more different, we expect agedifference to have a negative
effect on choice probabilities. The dummy variable genderf f (gendermm ) is
equal to one when the female (male) decision maker and the GP have the same
6
I am grateful to Sverre A. C. Kittelsen for pointing this out.
Surprisingly, 7 individuals had selected a GP in one of the other 13 municipalities in the
original data set. These individuals are excluded, and the corrected sample used for estimation
7
in the following sections contains 14993 individuals
10
gender, and zero otherwise. We see that 23% of sample are men who chose a male
GP while 38% are women who chose a female GP. In other words, 61% chose a
GP with the same gender and 39% selected a GP with different gender. We expect
genderii to have a positive effect on choice probabilities. The mean travel distance
between decision makers and the chosen GP is 2.64 kilometers and the mean travel
time is 0.04 hours. We also see that the mean travel cost associated with travel by
private car is e 1.42 whereas the mean travel cost associated with travel by taxi is
e 7.40.
Table 4: Descriptive statistics for the decision maker and chosen GP. Interaction
variables. N=14993
Variable
Mean
Std.dev
agedifference
genderf f
gendermm
kilometers
hours
cost CAR (e)
cost TAXI (e)
15.55
0.23
0.38
2.64
0.04
1.42
7.40
10.51
0.42
0.49
3.15
0.05
1.68
4.93
Min
0
0
0
0
0
0
0
max
58
1
1
25.10
0.37
13.08
36.56
4. Random utility and the nested logit model
The choice of GP is a qualitative choice. Due to computational feasibility and
convenience the most popular class of qualitative choice models is logit. The nested
logit model to be derived here is a generalization of the multinomial logit (MNL)
model described by McFadden (1974), and sometimes named McFaddens choice
model. We denote by Unj the utility consumer n obtains when selecting GP j.8
Utility is equal to the sum of a component, Vnj , that is a function of variables that
are observable and often called representative utility, and a component, εnj , that
is unobservable and random, and we have:
Unj = Vnj + εnj
8
This deduction follows closely that of Train (2003, p. 81-85)
11
(1)
The crucial part of the assumptions underlying the standard MNL model is that
the random factors, εnj , are uncorrelated over alternatives, as well as having constant variance across alternatives. In the context of this paper these assumptions
would require unobservable factors related to alternative GPs located in the same
neighborhood to be uncorrelated and have the same variance. One may argue that
two GPs located in the same neighborhood are likely to be closer substitutes as
compared to two GPs located in different areas. This kind of reasoning suggests
that it may be appropriate to specify a nested logit model where GPs who are close
substitutes are considered to belong to the same nest. Fortunately, it is straightforward to relax the restrictive assumptions underlying the standard MNL model and
specify a nested logit model where the MNL model is included as a special case.
The challenge is that an infinite number of nested logit models could be specified to
represent the situation at hand, as any given city can be divided into geographical
areas in an infinite number of ways. In particular, if one choose to specify a nest
structure with a small number of large areas with many alternatives in each nest,
one are less likely to place GPs that are close substitutes in different nests. On the
other hand, one is more likely to place GPs that are not close substitutes in the
same nest.
We now let the set of alternative GPs J be partitioned into K subsets denoted
B1 , B2 , ..., BK , j ∈ Bk ; k = 1, . . . , K and refer to the K subsets as nests. The
utility consumer n obtains when selecting GP j in nest Bk is equal to the sum of
the deterministic and stochastic part of utility as expressed by (1). The nested logit
model is obtained by assuming that the εnj ’s has a joint cumulative distribution
given by

exp −
K
X
k=1
Ã
X
!λk 

e−εnj /λk
j∈Bk
The parameter λk indicates the degree of independence in unobserved utility between alternatives within nest k. A higher value of λk indicates greater independence and less correlation. When λk = 1 for all k, representing independence among
all the alternatives in all nests, the nested logit model reduces to the MNL model.
Testing the hypothesis λk = 1 for all k is thus a valid test for the appropriateness
of the MNL model.
12
In this paper Vnj is specified as a linear function of observable variables:
Vnj = X nj β + Z j γ
where X nj and Z j are vectors of explanatory variables and β and γ are vectors of
the unknown parameters to be estimated. The latter parameters is assumed constant across nests, GPs and decision makers and may be interpreted as marginal
utilities within the random utility framework. X nj are explanatory variables interacting characteristics of the GP j with characteristics of consumer n, and Z j are
explanatory variables describing characteristics or attributes of GP j. In contrast
with X nj , Z j does not show any variation between decision makers, or in other
words, there are no “within alternative” variation in Z j . These vectors will include
the following variables:


X 0nj = 
genderf f
gendermm
agedifference
travel costs



, Z 0j = 




specialist
norwegianGP
marriedGP
ageGP
area1
..
.
areaK








nest
We see that the Z j vector include area indicators such that zjk
= 1 if GP j is part
of nest k. By estimating nest specific constants one ensure that the probability of
choosing a GP within nest Bk is consistently estimated. Conditioned on X nj , Z j ,
the probability that consumer n choose GP i can be expressed as:
Pni = P (Vni + εni > Vnj + εnj ; ∀i 6= j) = P (εnj < εni + Vni − Vnj ; ∀i 6= j)
A property of the nested logit model is that we get closed form expressions for Pni .
It can be shown that the probability of choosing GP i in nest Bk is given by:
¢
¡P
Vnj /λk λk −1
eVni /λk
j∈Bk e
Pni = P
,
¡P
¢
K
Vnj /λl λl
j∈Bl e
l=1
i, j ∈ Bk ; k, l = 1, . . . , K
In the next section we present the results from a nested logit model where
K = 5, that is, Oslo is divided in five nests by using postal codes. The Norwegian
Mail Service refers to the two first digits in this code as the postal code region. In
13
Oslo there are 12 different postal code regions9 : 01, 02, 03, . . . , 12. The postal code
region are used to define the five areas referred to as west, north, east1 , east2 ,
and south. The decision makers’ choice set is the complete set of GPs that where
actually available in Oslo when the regular GP scheme was implemented in June
2001, and all the decision makers are given identical choice sets. It should be noted
that specifying a rank ordered logit model (Beggs, Cardell and Hausman, 1981) and
utilizing the information on the alternatives ranked second and third was also considered. Although specifying such a model would allow us to extract more information from the data, extracting more information seems superfluous in the situation
at hand.10 Further, rank ordered logit models are vulnerable to heteroscedasticity
(Hausman and Ruud, 1987) as choices of the alternatives with lower ranking are
made more randomly. We therefore proceed and estimate a nested logit model by
means of the maximum likelihood method available in the software STATA version
10.
5. Estimation and results
The results from nested logit regression are reported in Table 5. Most of the estimated coefficients are statistically significant. The results confirm the result from
Lurås (2003) that GPs with specialist status have, cet. par., higher probabilities
of being chosen than non-specialists. We also see that the estimated effect of the
variables GP born in Norway and marriedGP are positive.
From the estimated effects of ageGP (positive effect) and agedifference (negative effect) we can make the interesting interpretation that consumers indeed do
prefer GPs with similar age, but a GP who is older is preferred to a GP who
is younger than oneself. An alternative interpretation of this result is that older
GPs are preferred to younger GPs, and that the size of this positive effect of
GP age is stronger the older the patient. The estimated effect of genderf f and
gendermm has the expected sign, supporting the idea that consumers prefer GPs
9
We ignore the postal code region 00 which is reserved for special addresses such as the royal
castle.
10
The author is also unaware of any standard software allowing for a nested specification of the
rank ordered model.
14
Table 5: Results from nested logit estimation
No. of cases=14993. No. of Alternative GPs=437. Total No. of Obs. 6551941
Taxi Travel Model
Regressor
Estimate
X nj variables
genderf f
gendermm
agedifference
costs TAXI
costs CAR
0.31
0.65
-0.02
-0.18
Z j variables
specialist
GP born in Norway
marriedGP
ageGP
west (ref. cat.)
north
east1
east2
south
Std.Err.
0.02**
0.03**
0.00**
0.00**
-
Car Travel Model
Estimate
Std.Err.
0.27
0.54
-0.02
0.02**
0.02**
0.00**
-
-0.51
0.01**
0.16
0.18
0.21
0.01
0.02**
0.02**
0.02**
0.00**
0.15
0.16
0.18
0.01
0.01**
0.02**
0.01**
0.00**
-0.08
-0.47
-0.72
-0.85
0.09
0.07**
0.09**
0.09**
-0.19
-0.33
-0.70
-0.56
0.09*
0.07**
0.08**
0.08**
Dissimilarity parameters (λk )
west
north
east1
east2
south
0.81
0.86
0.86
0.78
0.88
0.01**
0.03**
0.01**
0.02**
0.02**
0.72
0.76
0.73
0.67
0.69
0.01**
0.02**
0.01**
0.02**
0.02**
Log likelihood
P-value LR test for IIA
-68267.33
Prob > chi2 = 0.0000
-68128.09
Prob > chi2 = 0.0000
(*) significantly 6= 0 at the 5 % level (two tailed test)
(**) significantly =
6 0 at the 1 % level (two tailed test)
with the same gender. It is also interesting to compare the differences in magnitude of male and female consumers’ preferences for having a GP with the same
gender as expressed by the difference in the estimated effect of the two variables
genderf f and gendermm . The results indicate that male consumers have stronger
(p-value <0.01) preferences for having a GP with the same gender as compared to
female consumers. We observe that the area dummies assigned to three of the city
areas have significantly negative effect on choice probabilities. The interpretation is
that a practice located in the reference category west is considered to be favorable
by consumers. At the bottom of the table we observe the estimated values of the so
called dissimilarity parameters referred to as λk . These parameters are in the range
15
[0,1] in nested logit models that are consistent with random utility theory11 . The
value of the dissimilarity parameters indicate the degree of intra nest correlation in
unobserved utility, where values close to one imply low correlation and small values
indicate high correlation. We see that the values of these parameters range from
0.78 (north) to 0.88 (south), indicating that there are significant correlation in
unobservable utility associated with alternatives within each nest. In the special
case where λk = 1 for all k, the nested logit model collapse to the MNL model. At
the very bottom of the table we see that the hypothesis that λk = 1 for all k is
rejected, supporting the choice of a less restrictive nested logit model.
An application: Estimating the willingness to pay for GP attributes
Table 6: WTP estimates high-cost and low cost alternatives
Model
Variable
specialist
GP born in Norway
marriedGP
ageGP
genderf f
gendermm
agedifference
High-cost alternative: Taxi
WTP est. in e
0.89
0.99
1.15
0.07
1.71
3.55
-0.10
95 % Conf. Int.
0.72
0.79
0.98
0.06
1.50
3.28
-0.11
1.05
1.20
1.31
0.08
1.93
3.83
-0.09
Low-cost alternative: Private Car
WTP est. in e
0.29
0.31
0.35
0.02
0.53
1.07
-0.03
95 % Conf. Int.
0.23
0.25
0.30
0.02
0.47
0.98
-0.03
0.34
0.37
0.40
0.03
0.60
1.15
-0.03
The vectors β and γ may be interpreted as marginal utilities. Having an estimate of the marginal utility associated with the travel costs, we may derive an
estimate of the willingness to pay for attributes of GPs. This approach is often
referred to as the travel cost method, a method more frequently used in environmental economics (Parsons, 2003). By definition, a decision maker’s willingness
to pay for an attribute such as specialist status is the increase in travel costs that
keeps the decision maker’s utility constant given that GP specialist status “change”
from non-specialist to specialist. As described in Train (2003, p 43) we may take
the total derivative of utility with respect to travel costs and specialist status and
11
Dissimilarity parameters slightly larger than one are not necessarily inconsistent with random
utility theory. Dissimilarity parameters may never be negative, however. For discussions of
necessary and sufficient conditions for dissimilarity parameters to be consistent with random
utility theory consult Börsch-Supan (1990) and Herriges and Kling (1996).
16
set this derivative to zero as utility is kept constant:
∆ U = γ ∆ specialist+β ∆ travel costs= 0. Now we may solve for the
change in travel costs that keeps utility constant for a change in specialist status:
∆ travel costs
γ
=− .
∆ specialist
β
(2)
We note that the willingness to pay is positive as the cost coefficient γ is negative.
In Table 6 we have computed the willingness to pay estimates by using (2). The
standard errors of these ratios, which are needed to calculate the confidence intervals, are obtained by means of the delta method (Wikipedia contributors, 2009).
The disutility of the travel costs and the utility of the GP attributes is experienced at each consultation, and hence, the estimates presented in Table 6 denotes
the willingness to pay per consultation. The willingness to pay estimates resulting
from the Taxi Travel Model are higher than the estimates from the Car Travel
Model. Still the willingness to pay for consulting a specialist in general practice
appear to be low. When travel costs are calculated by means of taxi prices, the
estimated willingness to pay for specialist status of a GP amounts to only e 0.89
per consultation, whereas the estimated willingness to pay for having a GP with
the same gender amounts to respectively e 1.71 and e 3.55 for female and male
decision makers, respectively.
6. Discussion and conclusion
The value or importance that decision makers attach to each attribute of the
alternatives will in general vary. A limitation of the specified logit model is that it
is unable to handle random taste variation. One might argue that some decision
makers possess poor information on the concept of the specialist status, and hence
that estimating the same β and γ for all decision makers is a mis-specification.
Although random taste variation can be incorporated in mixed logit models, estimation of such a model with the present choice set does not seem feasible due to
the heavy computational burden. Estimation of a mixed logit model would most
likely require a significant reduction in the number of alternatives. In this paper we
have handled some elements of taste variation, by taking account of the possibility
that GP attributes such as gender do not affect a male decision maker in the same
17
way as a female decision maker, and by taking account of the fact that a young
patient may value high physician age differently than an elderly patient.
Some of the consumers may have chosen a GP located close to their workplace,
in order to combine everyday commuting with GP visits, and one may argue that
closeness to workplace should be included as a GP attribute. Multi-purpose trips
combining GP visits with commuting may imply that the computed travel costs are
slightly exaggerated for some of these consumers. However, the presented model
includes nest specific constant terms in the specification of representative utility
implying that the choice probabilities, and the effects of travel costs, are identified
by within-nest-variation in variables, and one may argue that unobservable effects
such as “high density of work places” in certain areas are controlled for.
In order to assess the robustness of the estimated parameters and corresponding
estimates of willingness to pay, several alternative models have been estimated.
First, a model with 12 nests (K = 12) corresponding to the 12 postal code regions
was estimated, and the results were compared with the above results. None of
the estimated willingness to pay estimates were significantly different from the
results presented here. The estimated dissimilarity parameters from the model
with 12 nests were quite different, however: Several dissimilarity parameters were
significantly larger than one, suggesting that the model might be inconsistent with
random utility theory, hence the simple 5 nest model is presented in this paper.
Second, the presented model was also estimated applying a random sample that was
not corrected for endogenous sample selection. It is interesting to note that none
of the estimated coefficients nor estimates of willingness to pay were statistically
different. The implication of this result is that, even if there is evidence that
the share of the population who took active part in the GP choice process differs
from the share who remained passive, there is no evidence suggesting that their
preferences for attributes of GPs are different.
There is evidence suggesting that consumers prefer GPs who resemble themselves on observable characteristics and it seems reasonable to conclude that the
consumer’s choice of GP is not random. Our estimates of the willingness to pay for
consulting a specialist in general medicine seems to indicate that the willingness
to pay is quite low and lower than the extra fee specialists in general medicine
received at the time. An interpretation is thus that that the authorities’ willing18
ness to pay is higher than that of the patients. Several scenarios may lead to such
an outcome. One particular scenario that is consistent with the presented results
is one where the a higher consultation fee is motivated by specialists being closer
substitutes to secondary care, and further, that specialists are expected to have
lower referral rates compared to non-specialists. The specialist status is indeed
valued by patients, and even more so by the authorities because fewer referrals to
secondary care means lower health care costs. In other words we may not conclude
that the situation at hand is one where the supply of specialist consultations are
higher than what is socially optimal.
Since 2005, part of the extra fee specialists receive is paid by the patient, in the
form of a e 3.30 patient co-payment. Since this co-payment rate is higher than the
willingness to pay estimates presented here, an idea for future research would be to
examine whether the introduction of a patient co-payment for consulting specialists
in general medicine has affected the demand for the services of these specialists.
Acknowledgements
Thanks to Eline Aas, Erik Biørn, Anne Hvenegaard, Tor Iversen, Sverre A. C. Kittelsen,
Hilde Lurås, Siri Fauli Munkerud and Erik Sørensen for suggestions that have contributed to
improvements of the paper. Thanks also to participants at The 28th Meeting of the Nordic
Health Economists’ Study Group, Tartu, August 2007 and The 7th European Conference on
Health Economics in Rome, July 2008, for helpful comments on a previous version of the paper.
Some of the data applied in this project are provided by the National Insurance Administration
and Statistics Norway. The data have been prepared for research purposes by The Norwegian
Social Science Data Services. The author alone is responsible for all analyses and interpretations
made in this text. Financial support from the Norwegian Ministry of Health and Care Services
and the Research Council of Norway through the Health Economics Research Programme at the
University of Oslo (HERO), is acknowledged. The author has no conflicts of interests with regard
to this research.
References
Beggs, S., S. Cardell, and J. Hausman (1981): Assessing the potential demand for
electric cars, Journal of Econometrics 16:1-19
Börsch-Supan, A., 1990, On the compatibility of nested logit models with utility
maximization, Journal of Econometrics 43: 373-388.
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Dixon, P., H. Gravelle, R. Carr-Hill and J. Posnett (1997): Patient movements and
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Hausman, J. and P. Ruud (1987): Specifying and testing econometric models for
rank-ordered data, Journal of Econometrics 34: 83-104.
Herriges, J. A. and C. L. Kling (1996): Testing the Consistency of Nested Logit
Models with Utility Maximization, Economics Letters 50: 3339.
Killi, M (1999): “Anbefalte tidsverdier i persontransport”, (In Norwegian) TØI
report 1999:459 Oslo.
Lurås, H., (2003): Individuals’ preferences for GPs Choice analysis from the establishment of a list patient system in Norway. HERO Working Paper 2003:
5.
McFadden, D., (1974): Conditional Logit Analysis of Qualitative Choice Behavior.
In P. Zarembka (Ed.), Frontiers in Econometrics,Academic press, New York.
Parsons, G.R. (2003): The travel cost model. In: Boyle, K., Peterson, G. (Eds.),
A Primer on Non-Market Valuation. Kluwer Academic Publishers, Dordrecht.
Rosenbaum, P. R., and D. B. Rubin (1983): The central role of the propensity
score in observational studies for causal effects. Biometrika 70: 41-55.
Ryan, M., E. Mclntosh and P. Shackley (1998): “Using conjoint analysis to assess
consumer preferences in primary care: An application to the patient health
card”, Health Expectations 1:117-129.
Ryan, M. and S. Wordsworth, (2000): “Sensitivity of willingness to pay estimates
to the level of attributes in discrete choice experiments”, Scottish Journal of
Political Economy 47: 504-524.
Scott, A. (2000): Economics of general practice. In A.J. Culyer and J.P. Newhouse
(Eds.) Handbook of Health Economics, Volume 1, Elsevier Science, Amsterdam,
1175-1200.
Scott, A. and S. Vick (1998): Agency in health care. Examining patients’ preferences for attributes of the doctor-patient relationship. Journal of Health Economics 17: 511-644.
Scott, A. and S. Vick (1999): Patients, doctors and contracts: An application of
principal-agent theory to the doctor-patient relationship. Scottish Journal of
Political Economy 46: 111-134.
Train, K. E., (2003): Discrete Choice Methods with Simulation. Cambridge university press, Cambridge.
van de Ven, W. and B. van Praag, (1981): “The Demand for Deductibles in Private Health Insurance: A Probit Model with Sample Selection”, Journal of
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20
Wikipedia contributors, (2009): “Delta method”, Wikipedia, The Free Encyclopedia, http://en.wikipedia.org/w/index.php?title=Delta method&oldid=270012701
(accessed March 11, 2009).
21
Appendix A:
Table A.1: Geographical representation of decision makers
Comparing the population means, with means from a random and a corrected sample
Postal Code
Dummies
02**
03**
04**
05**
06**
07**
08**
09**
10**
11**
12**
Population
N=401999
Mean
0.081
0.092
0.101
0.126
0.161
0.063
0.040
0.086
0.055
0.085
0.054
random sample
corrected sample
Participants only
Participants only
n=15000
Mean
0.077
0.086
0.098
0.117
0.171
0.069
0.042
0.089
0.049
0.103
0.056
n=15000
Mean
0.076
0.091
0.101
0.127
0.168
0.062
0.036
0.088
0.052
0.089
0.055
22
Table A.2: Results from Logit estimation
Estimating the probability of participating in the GP choice process. No. of obs. = 401999
Regressor
Female
Education1
Education2
Education3
Education4
Education5
Education6
Education7
Education8
Missingedu
Agecat2
Agecat3
Agecat4
Agecat5
Agecat6
Net Wealth
Decile1
Decile2
Decile3
Decile4
Decile5
Decile6
Decile7
Decile8
Decile9
Total Income
Decile1
Decile2
Decile3
Decile4
Decile5
Decile6
Decile7
Decile8
Decile9
Unemployd
cityarea2
cityarea3
cityarea4
cityarea5
cityarea6
cityarea7
cityarea8
cityarea9
cityarea10
cityarea11
cityarea12
europe
usacanada
africa
asia
oceania
southamerica
constant
Log likelihood
Pseudo R2
Coeff. Est.
0.670
0.093
0.060
0.265
0.339
0.340
0.478
0.518
0.526
-0.554
0.229
0.614
0.889
1.224
1.065
Std. Err.
0.008 **
0.063
0.047
0.047 **
0.047 **
0.052 **
0.047 **
0.048 **
0.062 **
0.049 **
0.010 **
0.012 **
0.013 **
0.017 **
0.016 **
-0.373
-0.338
-0.376
-0.389
-0.427
-0.157
0.006
0.095
0.096
0.017
0.018
0.018
0.018
0.019
0.019
0.019
0.019
0.019
**
**
**
**
**
**
**
**
**
-0.173
-0.150
0.005
0.114
0.219
0.247
0.266
0.216
0.150
-0.376
0.261
0.221
0.279
0.206
0.464
0.464
0.591
0.498
0.548
0.730
0.711
-0.155
-0.175
-0.390
-0.108
0.022
-0.581
-0.556
-227485.91
0.0975
0.018
0.018
0.018
0.018
0.018
0.017
0.017
0.016
0.016
0.012
0.019
0.018
0.018
0.017
0.017
0.021
0.024
0.019
0.021
0.020
0.021
0.014
0.043
0.023
0.015
0.144
0.041
0.053
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
23
Table A.3: Description of propensity score matching routine
Columns 1 and 4 records the estimated propensity score among non-participants in the random sample s with
15000 observations. Columns 2 and 5 reports the number of nonparticipants needed to be replaced. Columns 3
and 6 reports the number of matching candidates. We define a match when |ρ̂np − ρ̂p | < 0.01
ρ̂np
.07
.10
.12
.13
.14
.15
.16
.17
.18
.19
.20
.21
.22
.23
.24
.25
.26
.27
.28
.29
.30
.31
.32
.33
.34
.35
.36
.37
.38
.39
.40
.41
.42
.43
.44
.45
.46
.47
.48
.49
.50
.51
# to replace
1
1
2
1
8
3
9
7
4
6
7
12
9
20
17
17
14
29
35
28
30
34
27
30
42
54
40
51
53
48
55
61
68
63
78
71
93
74
88
81
85
121
# matching candidates
0*
10
9
20
29
30
27
63
43
55
87
95
89
118
171
127
137
215
244
236
193
282
318
431
476
511
631
621
644
744
878
995
1159
1136
1125
1226
1602
1577
1762
1753
1955
2376
ρ̂np
.52
.53
.54
.55
.56
.57
.58
.59
.60
.61
.62
.63
.64
.65
.66
.67
.68
.69
.70
.71
.72
.73
.74
.75
.76
.77
.78
.79
.80
.81
.82
.83
.84
.85
.86
.87
.88
.89
.90
.91
.92
.93
# to replace
118
135
99
103
134
125
117
110
128
130
114
129
107
124
124
137
137
120
100
109
122
98
103
99
114
99
87
87
128
85
72
101
81
68
76
66
66
62
31
16
21
11
# matching candidates
2435
2475
2275
2319
2917
3214
3049
3322
3180
3293
4026
3873
3657
3915
4617
5144
5369
4678
4707
5906
6127
5654
5917
5810
7191
6383
6864
7095
8386
7354
7439
8715
8059
8034
8579
7627
7097
6696
5084
3867
2718
1247
* No match was found for the non-participant with propensity score 0.07. This particular observation was matched with a candidate
with a propensity score of 0.08.
24